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We study the octonionic selfduality equations for $p=3$-branes in the lightcone gauge and we construct explicitly, instanton solutions for spherical andtoroidal topologies in various flat spacetime dimensions $(D=5+1,7+1,8+1,9+1)$,extending previous results for $p=2$ membranes. Assuming factorization of timewe reduce the self-duality equations to integrable systems and we determineexplicitly periodic, in Euclidean time, solutions in terms of the ellipticfunctions. These solutions describe 4d associative and non-associativecalibrations in $D=7,8$ dimensions. It turns out that for spherical topologythe calibration is non compact while for the toroidal topology is compact. Wediscuss possible applications of our results to the problem of 3-brane topologychange and its implications for a non-perturbative definition of the 3-braneinteractions.

On the Octonionic Self Duality equations of 3-brane Instantons